Finding the difference quotient?

Question

I am extremely confused. The direction reads:

Find the difference quotient

f(x+h) - f(x) / h and simplify your answer

1. f(x)=3x-4

2. f(x)=1-x^2

Can someone please explain this to me please. Thanks.

Answer 1

substitute in x + h, and find the value of the function... then subtract f(x), and divide the difference by h (then simplify where possible

1.  f(x + h) = 3(x + h) - 4 = 3x + 3h - 4

f(x) = 3x - 4

f(x + h) - f(x) = 3x + 3h - 4 - (3x - 4) = 3h

[f(x + h) - f(x) ] / h = 3

difference quotient for #1 is 3 (regardless of x or h...)

2) f(x + h) = 1 - (x + h)^2 = 1 - (x^2 + 2xh + h^2) = 1 - x^2 - 2xh - h^2

f(x) = 1 - x^2

f(x + h) - f(x) = 1 - x^2 - 2xh - h^2 - (1 - x^2) = -2xh - h^2

[f(x + h) - f(x)] / h = -2x - h

this value will vary with x and h...

Answer 2

     The difference quotient is the same as a derivative and you don't have to use that ridiculously long and useless formula to find it.  Use this equation: x^(n-1)*n.  

     So in 3x-4 n=1 because x is raised to the 1 power. So it would look like: 3x^(1-1)*1 which would be 3.  Therefore the difference qoutient is 3. Just ignore any constansts in the equations because they always turn into zero.  In my formula, 1-x^2 looks like: -x^(2-1)*2, and we ignore the 1 because it is only a constant.  So this ends up being -2x and that is the difference quotient.

Answer 3

ahah this is going to be fun when you learn the definition of a limit.

I think the other guy is solving it but good luck with this :)